# Absolute zero and Heisenberg uncertainty principle

I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position and momentum of the atom. We do know that Heisenberg uncertainty principle holds for microscopic particles in motion. But what then is wrong to consider that all molecular motion ceases at absolute zero? In other words, does the uncertainty principle not hold when there is no motion?

Need some help!

• I've read your question two times. I don't get what you're asking. Can you try to elaborate a bit further? I especially don't get your last sentence.
– seb
Commented Mar 7, 2013 at 8:58
• I mean to say that the heisenberg rule holds only 4 microscopic particle in motion...but at absolute zero motion is assumed to be absent...hope this helps... Commented Mar 8, 2013 at 20:08
• But movement does NOT cease - your assumption is wrong. Commented Sep 24, 2016 at 12:33
• I think he's talking about kinetic theory of gas , where such assumptions have been made as postulates to give a simplified version. Commented Nov 25, 2020 at 11:32

The situation is different for a free particle. In that case, at absolute zero the momentum is zero but then we have no knowledge about where the particle is (i.e. $\Delta x = \infty$). If we want to measure where the particle is we have to put some energy in, but then of course the system is no longer at absolute zero and the momentum is now non-zero.
The uncertainty principle is a fundamental property of quantum systems, and is not a statement about observational success. No particle either free or in crystal can have zero momentum otherwise a nonsensical infinity is required for the standard deviation of position $\Delta x$, in the uncertainty principle $\Delta x \Delta p \geq \hbar / 2$.
$0 \cdot \infty$ is undefined, so breaks the principle if the product is interpreted as zero. More likely the product should be interpreted as also undefinable, in which case the principle itself becomes undefinable. So all particles must move at least to some extent at all times or the uncertainty principle itself breaks down.